At issue is the timing of next year's fashion weeks, the biannual showcase for designers and brands to present their wares for the latest season.

Milan has announced that its fashion week next September will overlap those of New York and London, meaning that if no solution can be found, department store buyers and fashion magazine editors would be forced to choose one city over another.

Such a move could unravel the international web of advertising, retail, media and manufacturing interests on which the industry survives.

"There is a serious misunderstanding," said one source close to the situation. "But if we have to go head to head, then we will."

The dispute has grown over an agreement made between the fashion business syndicates of each city in 2008, which decreed that New York's fashion week would begin on the second Thursday of September, then followed consecutively by London, Milan and Paris.

British and American sources say the deal was meant to stand permanently, but the Italians and French claim it was only for three years. Earlier in the year, the Camera Nazionale della Moda Italiana, which runs Italian fashion and organises Milan, declared that its 2012 womenswear fashion week would begin on Sept 19. The French Federation de la Couture du Pret-a-Porter then announced it will begin its week on Tuesday, September 25, 2012.

Under the 2008 agreement, New York Fashion Week would start on Sept 13 and London on Sept 21.

A source said: "Each country has fashion industries worth a great deal of money to their respective economies. We need to collaborate, not go head to head. If we go head to head, all sides will end up losing out." Thus far, however, neither side has managed to find a compromise, despite a round of meetings between representatives of the four syndicates.

New York and London are understood to be preparing a direct appeal to the largest Italian fashion companies to reconsider, but have already received informal undertakings from some of the industry's largest retail and magazine interests that they will take precedence over Milan.

The final call, however, may well be made in Paris, as the two largest luxury goods conglomerates, LVMH and PPR, are both French.

Between them, the two groups own many of the biggest brands in fashion, including Alexander McQueen, Gucci, Marc Jacobs, Christian Dior and Louis Vuitton, giving them a near controlling-stake in magazine advertising and the production of clothing, accessories and fragrances.

Milan has already suggested to Paris that it brings its entire ready-to-wear fashion week forward from September to July, but the French syndicate rejected the proposal, saying it would compromise the Paris couture shows.

The real nub of the problem, say sources on both sides, is that the second Thursday in September falls so late next year, jeopardising production deadlines for meeting retail orders. It is this that has driven Milan into its decision to announce a clashing fashion week.

More broadly, the clash is symptomatic of a growing realisation that the old system of biannual fashion weeks is no longer in sync with a changed retail landscape.

Less than 30 per cent of buying is done at the fashion weeks, and the monthly magazines to which they are designed to appeal have been increasingly marginalised by an internet-led fashion consumer, typified by the success of the online retailer Net-a-Porter.

Money will be the deciding factor in this argument, and it's those two French conglomerates, LVMH and PPR, that have the most financial clout in fashion.

Whichever side they choose to support, egos will be bruised - even more than when the front row benches at Balenciaga collapsed here this week.

UPDATE
This morning the British Fashion Council issued this statement: "Camera Nazionale della Moda and Chambre Syndicale have announced dates for September 2012 that contravene the fashion week dates agreement of September 2008. We are in direct discussion with our counterparts and hope to resolve the matter over the next few weeks. We have a great deal of support from both international and domestic media and retailers in retaining the dates agreement."